The Mole (Amount of Substance)

Definition of the Mole

The mole is the unit used to measure the amount of substance in chemistry. It allows chemists to count particles like atoms, molecules, or ions by relating them to a standard number.

One mole contains exactly Avogadro's number of particles, which is:

$6.02 \times 10^{23}$

This number is so large because atoms and molecules are extremely small. Using the mole lets us work with amounts of substances in a manageable way, rather than counting individual particles.

For example, 1 mole of carbon atoms contains $6.02 \times 10^{23}$ carbon atoms.

Calculating Moles

You can calculate the number of moles of a substance using different methods depending on the information you have:

Using Mass and Relative Formula Mass

The number of moles ($n$) can be calculated from the mass ($m$) of a substance and its relative formula mass ($M_r$) using the formula:

$$n = \frac{m}{M_r}$$

- $n$ = amount of substance in moles ($\mathrm{mol}$)
- $m$ = mass of the substance ($\mathrm{g}$)
- $M_r$ = relative formula mass ($\mathrm{g\,mol^{-1}}$), the sum of the relative atomic masses of all atoms in the formula

For example, water (H₂O) has an $M_r$ of 18 (2 × 1 for hydrogen + 16 for oxygen).

If you have 36 $\mathrm{g}$ of water, the moles are:

$$n = \frac{36}{18} = 2\, \mathrm{mol}$$

For instance, if you have 10 $\mathrm{g}$ of sodium chloride (NaCl) with an $M_r$ of 58.5, the moles are:

$$n = \frac{10}{58.5} \approx 0.171\, \mathrm{mol}$$

Using Volume of Gases at Room Temperature and Pressure (RTP)

At RTP (room temperature and pressure), 1 mole of any gas occupies a volume of $24\,\mathrm{dm^{3}}$. You can calculate moles from the volume of gas using:

$$n = \frac{\text{volume of gas (dm}^3)}{24}$$

For example, 48 $\mathrm{dm^{3}}$ of oxygen gas contains:

$$n = \frac{48}{24} = 2\, \mathrm{mol}$$

Using Concentration and Volume of Solutions

For solutions, the amount of substance in moles can be found using concentration and volume:

$$n = \text{concentration (mol/dm}^3) \times \text{volume (dm}^3)$$

- Concentration is given in moles per cubic decimetre ($\mathrm{mol\,dm^{-3}}$)
- Volume must be in $\mathrm{dm^{3}}$ (1000 cm³ = 1 $\mathrm{dm^{3}}$)

For example, a 0.5 $\mathrm{mol\,dm^{-3}}$ solution with a volume of 0.2 $\mathrm{dm^{3}}$ contains:

$$n = 0.5 \times 0.2 = 0.1\, \mathrm{mol}$$

Avogadro's Constant

Avogadro's constant ($6.02 \times 10^{23}$) is the number of particles (atoms, molecules, ions) in one mole of any substance.

It links the microscopic scale (particles) to the macroscopic scale (moles), allowing calculations between the number of particles and the amount of substance.

The relationship is:

$$\text{Number of particles} = \text{moles} \times 6.02 \times 10^{23}$$

Or rearranged:

$$\text{Moles} = \frac{\text{Number of particles}}{6.02 \times 10^{23}}$$

For example, 2 moles of helium atoms contain:

$$2 \times 6.02 \times 10^{23} = 1.204 \times 10^{24} \text{ atoms}$$

If you know the number of particles, you can find the moles. For example, if a sample contains $3.01 \times 10^{23}$ molecules, the moles are:

$$n = \frac{3.01 \times 10^{23}}{6.02 \times 10^{23}} = 0.5\, \mathrm{mol}$$

Applications of the Mole Concept

The mole concept allows conversion between mass, moles, and number of particles, which is essential for quantitative chemistry.

You can:

• Convert mass to moles using $n = \frac{m}{M_r}$
• Convert moles to number of particles using Avogadro's constant
• Convert number of particles to moles by dividing by Avogadro's constant

This helps in understanding how much of a substance is involved in a reaction or sample.

For example, if you have 0.25 moles of sodium chloride (NaCl), the number of formula units is:

$$0.25 \times 6.02 \times 10^{23} = 1.505 \times 10^{23} \text{ formula units}$$